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In the given figure, O is the center of the circle. AB is the tangent to the circle at the point P. If ∠APQ = 58° then the measure of ∠PQB is
In the given Figure, Join OP
Now, OP ⏊ AB
[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]
∴∠OPA = 90°
∠OPQ + ∠APQ = 90°
∠OPQ + 58° = 90°
[Given, ∠APQ = 58°]
∠OPQ = 32°
In △OPQ
OP = OQ
[Radii of same circle]
∠OQP = ∠OPQ
[Angles opposite to equal sides are equal]
∠PQB = 32°
[As ∠OQP = ∠PQB ]